Problem: Simplify the following expression: $ x = \dfrac{-10z + 4}{-4z} + \dfrac{-3}{2} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-10z + 4}{-4z} \times \dfrac{2}{2} = \dfrac{-20z + 8}{-8z} $ Multiply the second expression by $\dfrac{-4z}{-4z}$ $ \dfrac{-3}{2} \times \dfrac{-4z}{-4z} = \dfrac{12z}{-8z} $ Therefore $ x = \dfrac{-20z + 8}{-8z} + \dfrac{12z}{-8z} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-20z + 8 + 12z}{-8z} $ $x = \dfrac{-8z + 8}{-8z}$ Simplify the expression by dividing the numerator and denominator by -8: $x = \dfrac{z - 1}{z}$